Question

Consider the following hypothesis test.

H₀: μ_d ≤ 0

H_a: μ_d > 0

(a)

The following data are from matched samples taken from two populations. Compute the difference value for each element. (Use Population 1 − Population 2.)

Element	Population		Difference
	1	2
1	21	20
2	28	28
3	18	18
4	20	18
5	26	24

(b)

Compute

d.

(c)

Compute the standard deviation

s_d.

(d)

Conduct a hypothesis test using

α = 0.05.

Calculate the test statistic. (Round your answer to three decimal places.)

Calculate the p-value. (Round your answer to four decimal places.)

p-value =

What is your conclusion?

Reject H₀. There is sufficient evidence to conclude that

μ_d > 0.

Do not Reject H₀. There is sufficient evidence to conclude that

μ_d > 0.

     Do not reject H₀. There is insufficient evidence to conclude that

μ_d > 0.

Reject H₀. There is insufficient evidence to conclude that

μ_d > 0.

Answer 1

Solution:Given null and alternative hypothesis are:

H₀: μ_d ≤ 0

H_a: μ_d > 0

First we create a table for calculation:

b) Here d = 1 which is average difference.

c) Standard deviation for difference = S_D​=1 .....Using excel formula, =STDEV(select difference column)

d)

This corresponds to a right-tailed test, for which a t-test for two paired samples be used.

Based on the information provided, the significance level is α=0.05, and the degrees of freedom are df = n -1 = 5 - 1 = 4

The p-value is p = 0.0445 . .........Using excel formula, =TDIST(2.236,4,1)

Since p = 0.0445 <0.05, it is concluded that the null hypothesis is rejected.

Conclusion:

Reject H₀. There is sufficient evidence to conclude that  μ_d > 0.

Done